Science for society

Understanding and reducing uncertainties in future global warming is essential for protecting societies and ecosystems. Human-driven CO2 emissions are the main cause of climate change, but the Earth-system response—how much additional warming results from each ton of emissions—remains uncertain. This study develops a new approach to narrow those uncertainties by accounting for feedbacks between the land, oceans, and atmosphere, especially under high-emission future scenarios. By improving the precision of global temperature projections, this work provides more reliable estimates of the “remaining carbon budget,” the total amount of CO2 that can still be emitted before crossing critical warming thresholds of 2°C and 3°C above preindustrial levels. These refined estimates help governments, businesses, and communities make better decisions when setting emission-reduction targets and preparing adaptation strategies. Our results highlight both opportunity and urgency. Even under the more optimistic constrained projections, global warming of 2°C could be reached within the next few decades. By reducing scientific uncertainty, our study empowers society to act with greater confidence. A clearer understanding of the risks and time frames ahead helps decision-makers avoid the dangers of delay and work toward a safer, more sustainable future for people and the planet.

Highlights

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We present an emergent constraint on future warming in response to carbon emissions

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The emergent constraint incorporates both climate and carbon-cycle feedbacks

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We reduce uncertainty in future warming and remaining carbon budgets for 2°C and 3°C

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Refined projections support effective climate mitigation and adaptation strategies

Summary

Reducing uncertainty in future temperature projections is crucial for understanding climate impacts of anthropogenic CO2 emissions and for guiding effective climate policy. This remains a complex challenge, as uncertainty in temperature projections arises from both climate and carbon-cycle feedbacks. Here, we introduce an observational constraint that integrates these feedbacks into emissions-driven simulations, reducing uncertainties in projected global temperature and effective transient climate response to cumulative CO2 emissions (eTCRE). Our approach lowers the projected mid-21st century eTCRE from 2.2°C (1.3°C–3.1°C) to 1.9°C (1.3°C–2.5°C) per 1,000 GtC. It also reduces projected end-of-century global temperature from 4.6°C (2.8–6.4°C) to 4.2°C (2.9°C–5.4°C) and refines estimates of the remaining carbon budget since 2020 for limiting warming to 2°C from 352.2 (2.1–702.3) to 458.9 (251.4–666.3) GtC under high-emission representative concentration pathway (RCP)8.5/shared socioeconomic pathway (SSP)5–8.5 scenarios. These refined projections provide critical insights for policymakers, enabling more effective mitigation strategies.

Graphical abstract

Keywords

1. emergent constraint
2. temperature projections
3. carbon cycle
4. remaining carbon budget
5. eTCRE

Introduction

The recent 6th Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) confirmed the near-linear relationship between cumulative CO2 emissions and the resulting increase in global surface air temperature (GSAT) throughout the 21st century.1,2 The transient climate response to cumulative CO2 emissions (TCRE; K GtC−1) describes this relationship and represents the ratio of the global temperature change to cumulative anthropogenic carbon emissions over time.3,4,5,6,7,8 TCRE is a critical metric for policymakers as it directly relates future emissions to projected levels of warming. Accurate quantification of TCRE is essential for predicting future warming under different policy choices and scenarios and for assessing the remaining carbon budgets that are necessary to stay within specific levels of warming.1,3,6 However, TCRE remains highly uncertain: the IPCC’s 6th Assessment Report best estimate is 1.65°C (1.0°C–2.3°C, likely 66% range) per 1,000 GtC. This means that if we add 1,000 GtC of carbon to the atmosphere, as projected under current emissions (11 GtC per year9), there is a 66% likelihood that mid-century warming from carbon emissions could be as low as 1°C or as high as 2.3°C. Under a very low-emission scenario (SSP1–1.9), this corresponds to 1.4°C (0.8°C–1.9°C) mid-century warming, whereas, under a very high-emission scenario (SSP5–8.5), this corresponds to 2.0°C (1.2°C–2.8°C) mid-century warming (note that these estimates exclude non-CO2 forcings). In practical terms, this uncertainty range spans outcomes from keeping warming below the Paris Agreement’s 1.5°C target to overshooting it substantially, with profound differences for climate impacts.

Uncertainty in the TCRE can be broken down into two components, reflecting different physical origins. First, the climate-carbon-cycle feedback determines the fraction of anthropogenic carbon emissions that remain in the atmosphere and is quantified by the airborne fraction.5,7,8,10 Uncertainties in this component arise from processes that control atmospheric carbon uptake by land and ocean. Second, the climate feedback is the relative change in GSAT driven by the change in atmospheric CO2 concentration, and is quantified by the transient climate response (TCR). Uncertainties in this component arise from physical parameters including radiative feedbacks and ocean-heat uptake efficiency. Both TCR and airborne fraction are scenario dependent and change over time because the efficiency of ocean-heat uptake and carbon sinks changes with the rate and magnitude of CO2 forcing, altering how the climate and carbon cycle respond under different emission pathways.11 Previous studies have shown that uncertainty in the TCRE is mainly caused by discrepancies in the TCR (accounting for up to 90% of the total variance in model-based analyses12), driven by the uncertainty in physical climate parameters, but variations in the carbon-cycle feedback are also important.5,7,8,10

TCRE and its drivers are estimated using Earth System Models (ESMs). Uncertainties and complexities in climate-carbon-cycle processes have resulted in a range of modeling choices in individual ESMs, which are collectively assessed via the Coupled Model Intercomparison Project (CMIP).13,14 Importantly, previous CMIP phases (including CMIP6) primarily compare ESMs using standardized future climate projections defined by projections of atmospheric greenhouse gas concentrations rather than emissions. In concentration-driven experiments, the GSAT change is determined by the TCR, while the carbon-cycle feedback is inferred by estimating compatible carbon emissions based on prescribed CO2 concentrations and the corresponding land and ocean carbon uptake.15,16 Since the GSAT change is determined by the TCR and does not include uncertainties in how the carbon cycle integrates anthropogenic emissions into the airborne fraction, previous CMIPs—and the IPCC Assessment Reports that have relied on them—have only incorporated one component of TCRE uncertainty. The ongoing 7th phase of CMIP (CMIP7) seeks to address the limitations of this approach and to better capture uncertainties in the carbon cycle by including the emissions-driven scenarios (representative emission pathways [REPs]) as a core focus.17,18 Consequently, even larger inter-model uncertainties are expected in the future temperature projections.

Emergent constraints are a promising tool for reducing uncertainty in climate projections. They rely on statistical relationships between historical and future ESM simulations and observational data.6,19,20,21,22,23,24 By identifying correlations between past and future model estimates that are rooted in physical mechanisms, emergent constraints align model outputs with observations, thereby improving the accuracy of future climate estimates. Several studies have constrained future climate projections using the historical temperature record, often by separating anthropogenic signals from natural variability through detection and attribution methods.8,19,20,21,25

This research builds on the studies that applied the emergent constraint framework to reduce uncertainties in TCR and cumulative carbon budgets for specific levels of global warming.6,19,20,25 Tokarska et al.20 showed that recent observed global temperature trends (T˙) can constrain projections of concentration-driven global mean temperature change (ΔTC). Likewise, Cox et al.6 demonstrated that the carbon budget up to the present day can constrain the remaining carbon budgets needed to meet the 1.5°C and 2°C targets of the Paris Agreement. Previously, Gillett et al.8 proposed a constraint on the TCRE by comparing historical warming with anthropogenic CO2 emissions, laying the foundational work for subsequent emergent constraint-based approaches. However, no previous studies have applied the emergent constraint approach to simultaneously constrain uncertainties in (1) temperature changes from emissions-driven experiments and (2) the corresponding TCRE. Addressing this gap is important because emissions-driven experiments explicitly couple the carbon cycle and climate systems. Constraining them jointly provides a more realistic basis for estimating the remaining carbon budget and guiding effective mitigation strategies.

Here, we present a method to constrain future emissions-driven temperature changes and TCRE values by incorporating past global warming trends (related to the TCR) and ratios of CO2 concentration increases between emissions-driven and concentration-driven historical simulations (related to the carbon-cycle feedback). We apply the emergent constraint framework to jointly constrain the physical and biogeochemical components of the Earth-system response. This approach effectively reduces uncertainties in future warming projections and carbon budgets. Specifically, it lowers the projected mid-21st-century eTCRE from 2.2°C (1.3°C–3.1°C) to 1.9°C (1.3°C–2.5°C) per 1,000 GtC, reduces projected end-of-century global temperature from 4.6°C (2.8°C–6.4°C) to 4.2°C (2.9°C–5.4°C), and refines the remaining carbon budget since 2020 for limiting warming to 2°C from 352.2 (2.1–702.3) to 458.9 (251.4–666.3) GtC under high-emission RCP8.5/SSP5–8.5 scenarios. Effectively reducing the uncertainty in future warming projections has wider implications for estimates of other geophysical20,22,26 and socio-economic27 variables whose changes are closely linked to future levels of global warming. Therefore, our results are relevant to impact-assessment studies as they improve the accuracy of projections of regional climate impacts and inform adaptation strategies in vulnerable regions, which is critical for both the scientific community and policymakers.

Results and discussion

Methods summary

We analyze historical and representative concentration pathway 8.5 (RCP8.5)/shared socioeconomic pathway 5–8.5 (SSP5–8.5) simulations. The RCP8.5 (used in CMIP5) and SSP5–8.5 (used in CMIP6) are high-emission scenarios, in which global warming is dominated by the CO2 forcing.28,29 The outputs from seven CMIP5 ESMs for RCP8.5 and 13 CMIP6 ESMs for SSP5–8.5 were available in both concentration- and emissions-driven setups (Tables S1 and S2). These paired configurations are particularly useful for comparing prescribed-concentration- and emissions-driven experiments, as they isolate the influence of carbon-cycle feedback on temperature responses under otherwise similar forcing conditions. The RCP8.5 and SSP5–8.5 scenarios are well suited for emergent constraint analyses because CO2 forcing dominates both past and future temperature changes, allowing a clearer detection of relationships between historical and projected Earth-system responses.

We focus on RCP8.5 and SSP5–8.5 scenarios rather than idealized experiments, such as the 1pctCO2 scenario, in which CO2 concentration increases 1% per year and which is often used in the emergent constraint studies.20,23,30 The RCP8.5 and SSP5–8.5 scenarios are more relevant for informing policymakers, and they are available in both concentration- and emissions-driven setups. Although both scenarios are labeled “8.5,” they differ in important aspects. The RCP8.5 and SSP5–8.5 follow distinct CO2 emissions and concentration pathways, with SSP5–8.5 reaching higher global CO2 emissions and concentrations by 2100.31 They also differ in land-use change (LUC) trajectories and in non-CO2 greenhouse gas and aerosol forcings, leading to differences in effective radiative forcing and slightly higher end-century warming under SSP5–8.5.21 Analyzing both scenarios is useful for emergent constraint development, as it allows testing whether relationships between past and future responses hold across different forcing compositions and model generations, while also increasing the sample size for more robust correlations. In our study, we treat RCP8.5 and SSP5–8.5 jointly for completeness but also examine the two scenarios separately in the supplementary analyses.

As the RCP8.5 and SSP5–8.5 scenarios include non-CO2 greenhouse gas and aerosol forcings, hereafter, we focus on the effective TCRE (eTCRE) concept (see methods). The eTCRE reflects the temperature response to cumulative carbon emissions but also accounts for the effects of non-CO2 gases and aerosols. Unlike the TCRE, which is typically estimated from idealized CO2-only scenarios, the eTCRE incorporates the influence of changing rates of emissions of non-CO2 climate forcers and is therefore more scenario dependent.32,33 Compared to TCRE, the eTCRE is generally higher and varies over time,6,33 providing a more realistic basis for developing emergent constraints in socially relevant emissions-driven scenarios.

In this study, we use the hierarchical emergent constraints framework22,27,34 (methods) by comparing simulated past GSAT trends with observations from the Hadley Center/Climatic Research Unit Temperature version 5 (HadCRUT5).35 This emergent constraint framework integrates both model and observational uncertainties using conditional probability distributions, where Bayes’ theorem is applied to derive a predictive distribution. Models are not excluded but instead are weighted by their consistency with observations, with less consistent models assigned lower likelihoods.34

Emergent constraints on global temperature projections

To better quantify and reduce uncertainties in future warming from the emissions-driven model simulations, we derive an emergent constraint on projected global mean temperature change. Previously, Tokarska et al.20 constrained the TCR and showed that models with higher recent past global temperature trends in concentration-driven simulations (denoted as T˙C, where the dot indicates a time derivative) tend to estimate larger future GSAT increases (ΔTC). The study analyzed ΔTC under high warming scenarios using CMIP5 and CMIP6 models and found strong positive correlations between T˙C and ΔTC, as both T˙C and ΔTC are dominated by greenhouse gas radiative forcing. Tokarska et al.20 used the range of temperature trends observed in the recent past to constrain the projected ΔTC. They found that ESMs that underestimate/overestimate past GSAT trends relative to observations tend to underestimate/overestimate future GSAT changes.

We first examine the emergent relationship, introduced by Tokarska et al.,20 shown in Equation 1, for an ensemble of CMIP5 and CMIP6 ESMs under RCP8.5 and SSP5–8.5 scenarios:

ΔTC∝T˙C.

(Equation 1)

We confirm a strong positive correlation (R = 0.75, p < 0.001) between past warming trends and future global temperature increases in concentration-driven simulations (Figure 1A). Incorporating observed past warming trends therefore enables the application of the emergent constraint framework (methods). When considering both scenarios, applying emergent constraints reduces the projected mean temperature increase by the end of the 21st century from 4.6°C (3.0°C–6.1°C) to 4.0°C (2.9°C–5.2°C) (Figure 1A), decreasing the variance by 47.4% (Figure S1A). The emergent constraint reduced the projected mean temperature increase by the end of the 21st century from 4.3°C (3.1°C–5.5°C) to 4.1°C (3.2°C–5.0°C) for RCP8.5 and from 4.7°C (3.1°C–6.4°C) to 3.9°C (2.7°C–5.1°C) for SSP5–8.5 scenarios (Figure S2A), decreasing their variances by 46.7% and 47.1%, respectively (Figure S1A).

Figure 1 Observational-constraint mechanism and observational constraint of future global surface air temperature changes

The vertical axes indicate the (A) future concentration-driven temperature change, ΔTC (°C); (B) ratio of the future CO2-induced radiative forcing change in emissions-driven and concentration-driven experiments, ln(CO2Efut)/ln(CO2Cfut) (unitless); and (C and D) future emissions-driven temperature change, ΔTE (°C) estimated by the CMIP5 and CMIP6 ESMs. The future changes are estimated for the 2081–2099 period under RCP8.5 and SSP5–8.5 scenarios. The horizontal axes show (A) past global (1980–2014) concentration-driven temperature trend, T˙C (°C per 35 years); (B) ratio of the past (2000–2014) CO2-induced radiative forcing change in emissions-driven and concentration-driven experiments, ψ (unitless); (C) past global (1980–2014) concentration-driven temperature trend adjusted by the ratio of the past (2000–2014) CO2-induced radiative forcing change in emissions-driven and concentration-driven experiments, T˙C×ψ (°C per 35 years); and (D) past global (1980–2014) emissions-driven temperature trend, T˙E (°C per 35 years). The black dashed horizontal and vertical lines in (B) indicate the level where the ratios equal one. In (A), (C), and (D), Pearson’s correlation coefficients and relative reduction of variance (RRV, %) for two scenarios combined (RCP8.5 and SSP5–8.5) are denoted at the bottom of the panels. Asterisks indicate that the correlations are significant at the ∗p < 5%, ∗∗p < 1%, or ∗∗∗p < 0.1% levels. The black dashed lines show the ordinary least-squares regression lines and the gray shadings indicate 95% confidence intervals. The horizontal boxplots indicate the mean (white line), 17%–83% range (box) and 5%–95% range (horizontal bar) of the observed temperature trends of HadCRUT535 estimated by Shiogama et al.36 (lavender). The vertical boxplots show the same as the horizontal boxplots but for the raw CMIP5 and CMIP6 models (black) and the constrained ranges using the observations (teal). Descriptions of the CMIP5 and CMIP6 models used are provided in Tables S1 and S2. The corresponding analyses for CMIP5 and CMIP6 models shown separately are presented in Figure S2.

The results described above, however, may also be influenced by internal climate variability. In particular, internal variability associated with the tropical Pacific surface warming pattern can modulate the relationship between past and future temperature changes, potentially affecting the strength of the emergent constraint. Although it has been suggested that such variability may affect the emergent constraint of ΔTC,37 it is difficult to distinguish between forced and internal variability components in the observed tropical Pacific surface warming pattern to date.38 Therefore, as a sensitivity test, Shiogama et al.27 simply doubled the variance of the internal climate variability added to the observed trends to account for the potential contributions of internal natural variability to the discrepancies between observations and ESMs. They found that the upper bounds of ΔTC can be lowered even with the doubled variance. We followed their approach and got similar results (Figure S1), confirming that our emergent constraint on future temperature projections is robust to the influence of internal climate variability.

While the TCR can be constrained from concentration-driven simulations alone, emissions-driven simulations introduce additional uncertainties arising from carbon-cycle processes. In particular, the temperature response in emissions-driven simulations is governed not only by the physical climate response but also by the fraction of emitted CO2 that remains airborne and by the land-ocean partitioning of the sink response. In addition, slow-responding components of the carbon cycle—such as long-term ocean dynamics and large-scale vegetation shifts—can manifest as delayed responses to past warming in emissions-driven simulations.7 These processes introduce further non-linearity into the system and motivate the explicit use of emissions-driven runs. These features vary across models and contribute to the spread in eTCRE. To explicitly separate these contributions, we introduce a set of intermediate equations that trace the propagation of uncertainty from carbon fluxes to temperature and show why applying a constraint in concentration-driven simulations is not sufficient for constraining warming under emissions-driven scenarios.

In both concentration-driven and emissions-driven RCP8.5/SSP5–8.5 scenarios, the future global temperature increase is primarily driven by CO2 forcing.31 Therefore, ESMs that project a larger increase in future CO2 concentration in emissions-driven compared to concentration-driven simulations are also expected to estimate a larger GSAT increase in emissions-driven runs, ΔTE, following Equation 2:

ΔTEΔTC∝ln(CO2Efut)ln⁡(CO2Cfut).

(Equation 2)

Here, CO2Cfut and CO2Efut indicate the ratios of the projected CO2 concentration (2081–2099 mean) and the reference preindustrial CO2 concentration in the concentration- and emissions-driven simulations, respectively. The ln(CO2fut) refers to the radiative forcing driven by the future change in CO2 concentration.39 We confirm this relationship using a suite of CMIP5 and CMIP6 ESMs (Figure S3A). There is a strong positive correlation (R = 0.88, p < 0.001) between the ratio of ΔT**E and ΔT**C and the corresponding ratio of CO2-induced radiative forcing. The range (difference between maximum and minimum values) of ln(CO2Efut)/ln(CO2Cfut) and ΔTE/ΔTC reaches 32.7% (from 85.3% to 118%) and 34.1% (from 84.9% to 119%), respectively, indicating the importance of accounting for the uncertainty in the carbon-cycle feedback (Figure S3A). The correlations remain statistically significant when CMIP5 and CMIP6 ESMs are analyzed separately under the RCP8.5 and SSP5–8.5 scenarios (Figure S3A).

In addition, we show a strong positive correlation (Figures 1B and S2B) between the ratios of CO2-induced radiative forcing in concentration-driven and emissions-driven simulations for the recent past (2000–2014) and the future (2081–2099) periods, as described in Equation 3:

ln(CO2Efut)ln⁡(CO2Cfut)∝ln(CO2Epast)ln⁡(CO2Cpast).

(Equation 3)

Here, CO2Epast is the ratio of the estimated past and the reference preindustrial global mean CO2 concentration by CMIP5 and CMIP6 ESMs, and CO2Cpast refers to the prescribed ratio of past and preindustrial CO2 concentrations.40,41 For simplicity, we define the ratio of CO2 radiative forcing between emissions-driven and concentration-driven simulations as ψ.

ψ=ln(CO2Epast)ln(CO2Cpast).

(Equation 4)

This diagnostic variable captures model differences in airborne fraction and sink partitioning, allowing us to explicitly trace how carbon-cycle uncertainty contributes to warming spread in emissions-driven simulations. Models that estimate a higher/lower airborne fraction in the past tend to estimate a higher/lower airborne fraction in the future. This relationship provides a basis for constraining carbon-cycle feedback in emissions-driven simulations.

By combining Equations 1, 2, 3, and 4, we can derive Equation 5, which can be used to constrain future emissions-driven global warming projections:

ΔTE∝T˙C×ψ.

(Equation 5)

In Figure 1C, we show a strong positive correlation (R = 0.75, p < 0.001) between the future GSAT increase in the emissions-driven simulations and the past concentration-driven GSAT trends, when adjusted by the ratio of CO2 radiative forcing between emissions- and concentration-driven simulations, ψ. The correlation remains significant (at 5% level) when analyzing CMIP5 and CMIP6 ensembles separately (Figure S2B). In this context, the estimates of past concentration-driven global temperature trends, T˙C, reflect each model’s representation of the climate feedback, while the ratio of past CO2-induced radiative forcing, ψ, indicates the strength of the carbon-cycle feedback. By considering both past temperature trends and the radiative forcing ratio, we can achieve a 50.4% reduction in the inter-model variance of ΔTE, and lower the mean value (5%–95% range) of ΔTE from 4.6°C (2.8°C–6.4°C) to 4.1°C (2.9°C–5.3°C) under the RCP8.5 and SSP5–8.5 scenarios combined (Table S3). When we use only T˙C, the relative reduction of variance (RRV) decreases to 41.6% (Figures S1C and S3C), indicating that it is important to take into account ψ as well as T˙C for effective emergent constraint. Our results remain robust when analyzing a smaller set of only CMIP5 or CMIP6 models (Figure S3; Table S3). This emergent constraint lowers the ΔTE from 4.6°C (2.8°C–6.4°C) to 4.2°C (2.9°C–5.5°C) and from 4.7°C (2.9°C–6.4°C) to 3.9°C (2.7°C–5.1°C) under the RCP8.5 and SSP5–8.5 scenarios, respectively. Even when the variance in the observational uncertainty range is doubled, the uncertainties in emissions-driven global temperature projections can still be effectively reduced (Figure S1B).

Extending the framework described by Equations 1, 2, 3, 4, and 5, we show that it is also possible to constrain future global temperature projections using past warming trends in the emissions-driven simulations (Figure 1D). We find a strong correlation between the past warming trends in the emissions-driven simulations (T˙E) and those in concentration-driven simulations adjusted by the carbon-cycle feedback (T˙C×ψ) (R = 0.74; Figure S3B), as described by Equation 6:

T˙E∝T˙C×ψ.

(Equation 6)

Combining Equations 5 and 6, we can expect that future projected warming is well correlated with past GSAT trends in emissions-driven simulations (T˙E), according to Equation 7:

ΔTE∝T˙E.

(Equation 7)

We confirm this relationship in Figure 1D (R = 0.76) across RCP8.5 and SSP5–8.5 scenarios together, as well as within each scenario separately (Figure S2D). This emergent constraint can lower the mean and reduce the uncertainty range of ΔTE from 4.6°C (2.8°C–6.4°C) to 4.2°C (2.9°C–5.4°C) (Table S3). This reduces the variance by 51.7% (Figure S1D), which is similar to the 50.4% reduction achieved by the emergent constraint in Equation 5. When analyzing scenarios separately, the constrained projected end-of-century global temperatures are 4.1°C (2.8°C–5.4°C) and 4.2°C (3.0°C–5.4°C) under RCP8.5 and SSP5–8.5, respectively (Table S3). Note that, alongside the scenario differences themselves, the variations in ESM ensemble sizes contribute to the differences in the constrained projections in two scenarios.

We confirm that our results are not sensitive to the choice of observational data and past temperature trend period by repeating the analysis using the GISTEMP442 observational dataset and six alternative windows ranging from 30 to 50 years (Figure S4; Table S4). The emergent relationship remains strong and statistically significant (at 1% level) across all cases (R = 0.66–0.83), with relative variance reductions of 47%–58% (identical for the two observational datasets).

Emergent constraints on eTCRE

Using prescribed carbon emissions from the RCP8.5 and SSP5–8.5 scenarios, alongside constrained temperature change projections (Figure 2B), we are able to refine estimates of the eTCRE (Figure 2A, 2C, S5A, and S5C) (methods). ESMs that overestimate the past emissions-driven CO2 increase also tend to overestimate future global temperature change in the emissions-driven simulations (Figure 2B). Consequently, the eTCRE can be constrained from 2.2°C (1.3°C–3.1°C) per 1,000 GtC to 1.9°C (1.3°C–2.5°C) per 1,000 GtC, and the variance can be reduced by 50.3% for the RCP8.5 and SSP5–8.5 scenarios combined (Figures 2A and 2C; Table S5). The constrained results indicate that, under high-emission scenarios, the 2°C global temperature threshold will be reached by 2045 (2033–2065), compared to 2038 (2021–2065) for the unconstrained estimate (Figure 2B). For the individual scenarios, the constraints similarly narrow the range of eTCRE and delay the timing of the 2°C threshold. Under RCP8.5, the eTCRE is reduced from 2.3°C (1.3°C–3.3°C) to 2.1°C (1.6°C–2.6°C) per 1,000 GtC (RRV = 72.2%), while, under SSP5–8.5, it decreases from 2.1°C (1.3°C–2.9°C) to 1.8°C (1.8°C–2.4°C) per 1,000 GtC (RRV = 50.4%). Despite differences in ensemble size and scenario design, both cases indicate a constrained 2°C crossing around the mid-2040s (2045 under RCP8.5, 2047 under SSP5–8.5), with narrower uncertainty ranges compared to the unconstrained estimates (Figure S5B). The proposed emergent constraint remains effective at least until the end of the 21st century under scenarios of continued CO2 increase driven primarily by fossil fuel emissions. Due to the limited availability of emissions-driven ESM outputs for climate change mitigation and overshoot scenarios in CMIP5 and CMIP6 models, we are unable to verify the applicability of the emergent constraint to different scenarios, such as those aiming for temperature stabilization. This verification should be continued in future CMIP7 simulations. The proposed emergent constraint may not be appropriate for scenarios in which radiative forcing and carbon-cycle feedbacks are strongly influenced by non-CO2 forcings or non-CO2 climate change mitigation options, such as solar-radiation modification.

Figure 2 Observational constraints on the future changes in GSAT and eTCRE

(A) The vertical axes indicate the emissions-driven effective TCR to cumulative CO2 emissions (eTCRE), eTCREE (°C per 1,000 GtC) estimated for the future 2081–2099 period under RCP8.5 and SSP5–8.5 scenarios by CMIP5 and CMIP6 ESMs, and the horizontal axes indicate past global (1980–2014) concentration-driven temperature trends adjusted by the ratio of the past (2000–2014) CO2-induced radiative forcing change in emissions-driven and concentration-driven experiments (°C per 35 years). Pearson’s correlation coefficients and relative reduction of variance (RRV, %) for two scenarios combined (RCP8.5 and SSP5–8.5) are denoted at the bottom of the panel. Asterisks indicate that the correlations are significant at the ∗p < 5%, ∗∗p < 1%, or ∗∗∗p < 0.1% levels. The black dashed line shows the ordinary least-squares regression line, and the gray shading indicates its 95% confidence interval. The horizontal boxplot indicates the mean (white line), 17%–83% range (box), and 5%–95% range (horizontal bar) of the observed temperature trends of HadCRUT535 estimated by Shiogama et al.36 (lavender). The vertical boxplots show the same as the horizontal boxplots but for the raw CMIP5 and CMIP6 models (black) and the constrained ranges using the observations (teal).

(B and C) Time series of emissions-driven temperature change, ΔTE (°C), plotted against (B) time (year) and (C) cumulative over time (from 1850) carbon emissions (GtC) for each CMIP5 and CMIP6 model. The constrained ranges in all panels are estimated for the future mean temperatures during 2035–2054 (the 20-year period when cumulative carbon emissions reach approximately 1,000 GtC) and then are scaled across the entire period for the (B) and (C). The black lines indicate the mean, and the teal shadings indicate the 5%–95% constrained range. The black dashed horizontal lines indicate 2°C warming, relative to 1850–1899 levels. Descriptions of the CMIP5 and CMIP6 models used are provided in Tables S1 and S2. The corresponding analyses for CMIP5 and CMIP6 models shown separately are presented in Figure S5.

Emergent constraints on the remaining carbon budget

Having constrained the warming response to cumulative CO2 emissions, we next use this relationship to infer the remaining carbon budget consistent with specific temperature limits. Using the available emissions-driven simulations, RCP8.5 and SSP5–8.5, we apply the emergent constraint to estimate the remaining carbon budget consistent with given temperature targets (Figures 3A and S6; Table S6 for the 2°C target, see also Figure S7; Table S7 for the 3°C target). Note that, unlike eTCRE, which relates to cumulative emissions since preindustrial times, the remaining carbon budget starts from present-day warming levels (defined as the 2000–2014 mean warming in emissions-driven simulations relative to 1850–1899 mean). As both eTCRE and present-day warming vary across models, the resulting remaining carbon-budget estimates do not scale directly with the eTCRE ratio alone.

Cox et al.6 constrained the remaining carbon budget using the emergent relationship between cumulative emissions and temperature increase up to 2020 in concentration-driven simulations. In contrast, we use global temperature trends in emissions-driven simulations (methods). These two measures of past change—the concentration-driven carbon budget to the present day by Cox et al.6 and our emissions-driven past temperature trends—are negatively correlated (R = −0.69, p < 0.001; Figure S8). Our emergent constraint refines the mean (5%–95% range) remaining carbon budget for 2°C warming from 352.2 (2.1–702.3) GtC to 458.9 (251.4–666.3) GtC (with a 17%–83% likely range of 338.6–579.2 GtC) across the combined CMIP5 and CMIP6 ensembles (RRV = 64.9%; Table S6). When analyzed separately, the constrained budgets are 481.9 (272.2–691.6) GtC for CMIP5 (RRV = 76.1%) and 444.1 (249.4–638.7) GtC for CMIP6 (RRV = 57.6%). These constrained values align with the estimates of Cox et al.6 for concentration-driven runs (422 GtC with a likely range of 258–586 GtC). Notably, our constraints are narrower than the estimates of Cox et al.6 by using different simulations (Cox et al. use the concentration-driven simulations, while we use the emissions-driven simulations), despite using a larger set of models. We show that the remaining carbon budget for a given temperature target by the end of the 21st century can be constrained by the past temperature trends.

Our constrained estimates of the remaining carbon budget also compare well with the IPCC 6th Assessment Report assessed carbon budgets (Table SPM.2 of the IPCC 6th Assessment Report2), which combine multiple lines of evidence rather than relying on raw CMIP ensembles. For the 2°C target, the IPCC 6th Assessment Report states a median remaining budget of 368 GtC with a 17%–83% range of 246–627 GtC, which lies within our constrained distribution but with a narrower spread. Our emergent constraint method, therefore, produces budgets closer to the 6th Assessment Report than to the unconstrained CMIP range, while shifting the midpoint upward compared to AR6. This suggests that incorporating past emissions-driven warming trends can both reduce raw model spread and refine the central estimate, complementing the multi-line-of-evidence assessment used in the IPCC 6th Assessment Report.

Like Cox et al.,6 our method can constrain the eTCRE and the associated remaining carbon budget, which are key metrics for informing mitigation policy by refining estimates of allowable cumulative CO2 emissions consistent with temperature goals (e.g., 1.5°C or 2°C). Additionally, by providing the emergent constraint on the uncertainty in the global mean temperature change, our approach can narrow the uncertainty ranges in projected changes in other climate variables (e.g., precipitation changes, regional temperature and precipitation extremes)22,26 and the carbon-cycle responses (e.g., of the Amazon rainforest).43 This improved consistency among temperature and impact projections can also reduce uncertainty in downstream economic impact assessments,27 thereby providing more robust information for adaptation planning and risk management.

Mechanisms of emergent constraints on carbon budget

As most ESMs provide simulation output for both land (accounting for LUC emissions) and ocean carbon sinks, we can perform a detailed analysis to refine the partitioning of future carbon emissions between these reservoirs. This approach allows us to better understand how emissions are distributed between land, ocean and the atmosphere (Figures 3B and S6–S8) (methods). Note that, due to the lack of carbon flux data for some ESMs and the presence of residual sink/source terms,44 the sum of these carbon pool components does not perfectly align with anthropogenic carbon emissions. The emergent constraint based on the historical temperature trend in the emissions-driven simulations, T˙E, allows the variance in the remaining carbon budget distributions to land, ocean and atmosphere to be reduced by 30.5%, 50.8%, and 67.5%, respectively, for the 2°C target under RCP8.5 and SSP5–8.5 scenarios combined (Figures 3B and S9). The emergent constraint allows the mean (5%–95% range) cumulative carbon uptake by land, ocean and atmosphere from the year 2020 to the year when the 2°C warming level is reached to increase from 58.4 (−87.7–204.5) GtC, 77.9 (−16.5–172.3) GtC, and 184.5 (5.1–363.9) GtC to 86.8 (−35–208.6) GtC, 101.6 (35.4–167.7) GtC, and 236.3 (134–338.6) GtC, respectively.

We propose the following mechanism underlying this emergent constraint. Many ESMs overestimate past global temperature trends and future temperature increases in the emissions-driven simulations (Figure 1D). This leads to an earlier reaching of the target temperature threshold (Figure 2B). As a consequence, the cumulative carbon uptake by land and ocean—currently acting as carbon sinks45—tends to be underestimated (Figures 3, S6 and S7).

The relationships between the carbon pools of land, ocean, and atmosphere and T˙C×ψ for 2°C show strong negative correlations for ocean and atmosphere, although, for land, the correlation remains negative but weaker (Figure S10). We attribute the changes in land and ocean carbon reservoirs for the 2°C carbon budget to climate feedback (∝T˙C) and carbon-cycle feedback (∝ψ). Breaking down the relationship between cumulative carbon sinks (land, ocean, and atmosphere) and T˙C×ψ (Figures S10A–S10C) reveals strong negative correlations between cumulative carbon sinks in the ocean and atmosphere and T˙C (Figure S10). Furthermore, all three carbon pools—land, ocean, and atmosphere—show strong negative correlations with ψ (representing the carbon-cycle feedback; Figures S10G–S10I). From the magnitude of the correlations, we infer that the climate feedback (∝T˙C) dominates changes in the ocean and atmospheric carbon pools, while the carbon-cycle feedback (∝ψ) has a stronger influence on the land carbon pool. These results are consistent with a previous study that highlighted the large inter-model spread in estimates of the land carbon sink, which is rooted in uncertainties in the carbon-cycle feedback.10 In emissions-driven simulations, this spread reflects not only differences in climate response but also variations in the representation of land processes such as dynamic vegetation, soil carbon turnover, and nutrient limitations—particularly nitrogen constraints on plant productivity.7,8,10 These land processes critically shape the strength of the terrestrial carbon sink and amplify uncertainty in projections of the remaining carbon budget. The limitations in nitrogen and phosphorus availability can strongly suppress CO2 fertilization effects, especially in high-latitude and tropical ecosystems, while soil process representations influence the longevity of carbon storage.15 Moreover, model differences in LUC dynamics further compound this uncertainty.46 Addressing these processes in ESMs remains a major research challenge for narrowing the spread in future land carbon-sink projections. Finally, both climate and carbon-cycle feedbacks act additively, reinforcing the strength of the emergent constraint, as shown in Figures 3B and S5B.

Even the more optimistic estimates of land and ocean carbon uptake refined in this study suggest that the 2°C warming will be achieved within the next few decades, assuming current annual carbon emission rates of 11 GtC per year.6,45 While our constrained estimates point to a somewhat larger remaining carbon budget compared to the raw ensemble mean, this should not be interpreted as a buffer for delayed action. Continued high emissions will rapidly consume the remaining budget, increasing the likelihood of temperature overshoot and associated climate risks. This underscores the need for more stringent mitigation strategies to reduce atmospheric carbon.

In this study, we refer to the land carbon component of the remaining carbon budget, which includes LUC emissions. The LUC emissions cannot be isolated in our analysis because many ESMs do not provide outputs for LUC emissions, and definitions of LUC vary between models.44,47 We verified that the results remain consistent when considering only the subset of ESMs (nine out of 20) that report simulated LUC emissions. A corresponding analysis based on these models yields constrained eTCRE values that are in line with the findings presented in this study (not shown). Including more consistent LUC emissions, especially their gross values, would enable further analysis of how future changes in land and ocean carbon-cycle feedbacks influence the remaining carbon budget. In addition, including pairs of consistent idealized concentration-driven and emissions-driven experiments in CMIP7 would facilitate the analysis of TCRE components (including carbon-cycle and climate feedbacks), complementing the eTCRE uncertainties addressed in this study. We further encourage that the upcoming Land Use Model Intercomparison Project (LUMIP) experiments in CMIP748 be used to provide more consistent and detailed representations of LUC, thereby enabling a more comprehensive assessment of its role in TCRE and remaining carbon budget estimates.

Implications and limitations of the emergent constraints

While our emergent constraint is derived under high-emission scenarios (SSP5–8.5 and RCP8.5), it provides a proof of concept for how constrained estimates of remaining carbon budgets can be obtained directly from ESMs with interactive carbon cycles. Notably, our constrained estimate of eTCRE lies well below most individual ESM values (Figure 2A), with over two-thirds of models projecting higher values than what is supported by historical observations. This highlights a potential overestimation of future warming in raw model ensembles and emphasizes the importance of incorporating observational constraints to refine projections. However, we caution that this does not reduce the urgency of mitigation: under current emissions, the time window to remain within the 2°C target remains narrow, even when using the upper end of the constrained carbon budget range. As emissions-driven simulations under a broader range of scenarios become available in CMIP7, the approach demonstrated here can be extended to quantify scenario-specific eTCRE values and carbon budgets and tested under deep mitigation or overshoot pathways. This will be particularly valuable for producing observationally constrained projections tailored to the more policy-relevant scenarios of the next IPCC assessment.

Our emergent constraint is implicitly conditioned on the radiative forcing composition of the historical period, where aerosol and greenhouse gas forcings have opposing effects. The relationship between airborne fraction, warming, and cumulative emissions may be sensitive to the evolving ratio of greenhouse gas to aerosol forcing. If this ratio shifts substantially in the future—for instance, due to rapid greenhouse gas and aerosol reductions—then the emergent constraint calibrated on historical dynamics may not apply cleanly. This limitation is shared with other observationally constrained projections,19,20 and we highlight this issue as an important caveat for interpreting constrained warming under deep mitigation or overshoot scenarios.

Conclusions

In this study, we constrain future temperature projections in emissions-driven ESM simulations by accounting for uncertainties in both climate and carbon-cycle feedbacks. We introduce an emergent constraint that leverages historical temperature trends from concentration-driven experiments and past changes in atmospheric CO2 concentration driven by carbon-cycle feedbacks observed in emissions-driven experiments. This approach allows for constraining the projected temperature increase under high-end scenarios by the end of the 21st century, ΔT**E. Our framework not only refines temperature projections but also allows for reducing uncertainty in estimates of future eTCRE and specific carbon budget for a given temperature target under high-emission RCP8.5 and SSP5–8.5 scenarios. We successfully constrain the mean (5%–95% range) ΔT**E from 4.6°C (2.8°C–6.4°C) to 4.2°C (2.9°C–5.4°C), the projected eTCRE from 2.2°C (1.3°C–3.1°C) to 1.9°C (1.3°C–2.5°C) 1,000 GtC−1, and the remaining carbon budget since 2020 for 2°C warming from 352.2 (2.1–702.3) to 458.9 (251.4–666.3) GtC.

We present a simple approach to address uncertainties in temperature-change projections based on anthropogenic carbon emissions and the implications for the remaining carbon budget, providing important insights for the scientific community and policymakers. It equips the CMIP7 community with a valuable method for improving the accuracy of model projections, thereby contributing to more reliable climate predictions. Our constrained estimates also tend to reduce the upper bound of projected warming and eTCRE values, aligning more closely with historical observations and reinforcing the importance of model evaluation against real-world data. Furthermore,